Mixing, enthalpy Gibbs energy

For a perfect binary solution the free enthalpy (Gibbs energy) of mixing per mole has been given in Eq. 8.7. We extend this equation 8.7 to a non-ideal binary solution by using the activity coefficients and y2 as shown in Eq. 8.17 ... 

The heat of mixing (excess enthalpy) and the excess Gibbs energy are also experimentally accessible, the heat of mixing by direcl measurement and G (or In Yi) indirectly as a prodiicl of the reduction of vapor/hqiiid eqiiihbriiim data. Knowledge of H and G allows calculation of by Eq. (4-13) written for excess properties. 

Figure 3.3 Thermodynamic properties of an arbitrary ideal solution A-B at 1000 K. (a) The Gibbs energy, enthalpy and entropy, (b) The entropy of mixing and the partial entropy of mixing of component A. (c) The Gibbs energy of mixing and the partial Gibbs energy of mixing of component A.

Figure 11.13 (a) Enthalpy, (b) entropy and (c) Gibbs energy of mixing of MnO-MgO at 1000 K, all calculated using the configurational averaging technique. 

Numerical parameter employed in the Flory-Huggins theory, to account for the contribution of the noncombinatorial entropy of mixing and the enthalpy of mixing to the Gibbs energy of mixing. 

In equation 33, the superscript I refers to the use of method I, a T) is the activity of component i in the stoichiometric liquid (si) at the temperature of interest, AHj is the molar enthalpy of fusion of the compound ij, and ACp[ij] is the difference between the molar heat capacities of the stoichiometric liquid and the compound ij. This representation requires values of the Gibbs energy of mixing and heat capacity for the stoichiometric liquid mixture as a function of temperature in a range for which the mixture is not stable and thus generally not observable. When equation 33 is combined with equations 23 and 24 in the limit of the AC binary system, it is termed the fusion equation for the liquidus (107-111). 

Once the species present in a solution have been chosen and the values of the various equilibrium constants have been determined to give the best fit to the experimental data, other thermodynamic quantities can be evaluated by use of the usual relations. Thus, the excess molar Gibbs energies can be calculated when the values of the excess chemical potentials have been determined. The molar change of enthalpy on mixing and excess molar entropy can be calculated by the appropriate differentiation of the excess Gibbs energy with respect to temperature. These functions depend upon the temperature dependence of the equilibrium constants. 

This reaction stops when the liquid composition reaches point J, where SiC becomes stable in contact with the liquid and precipitated C. At this point, the equilibrium molar fraction of Si dissolved in M, X (Figure 7.2), is related to the partial enthalpy of mixing of Si in M, AHsi(M) (neglecting the partial excess entropy of mixing), and to the molar Gibbs energy of formation of SiC, AGf(SiC), by the equation ... 

Mass spectrometric studies (1.-5) of the equilibrium gases over pure KOH(cr, t) and mixed KOH-NaOH condensed phases have unequivocally identified the vapor species as monomer and dimer in the temperature range 600-700 K. Absolute partial pressures for KOH(g) and K2(OH)2 (g) have been determined from peak intensity data by Porter and Schoonmaker (3 ) and Gusarov and Gorokhov (5). These data are analyzed by the 3rd law method with JANAF Gibbs energy functions (6) in order to evaluate an enthalpy of dimerization at 298 K. The adopted value is A H (298.15 K) = -45.3 t 3.0 kcal mol" for the reaction 2 KOH(g) = K2(0H)2 (g). 

AlN ubic Naci Table 1) as well as the mixing enthalpy of AlN-TiN cubic NaCl solutions. These values, together with the calculated value for the Gibbs energy difference between the NaCl and wurtzite structural forms of pure UN, allow a thermodynamic analysis of the TiN-AlN system to be made. 

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